Struggling to model irregular rounded shape, any recommended tips/tutorials?
Assuming this is an exercise; that you're not wanting to retopologise the original in some radically different way..
This is a subdiv. model: the topology is a that of a Round Cube.
So, starting with 1/4 of one of those, mirrored left to right, and keeping the poly count at the minimum to capture the curvature:

.. just shovel the vertices around under proportional editing, while looking at the result under Catmull-Clark subdivision, level 2. You could use a more orthogonal reference, for accuracy.

Add a Solidify modifier for thickness, creasing the rim, and, after applying the modifiers, extrude the fillet.